Altitudes in Right Triangles Practice

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Sarah is building a dog house. She has created the rectangular house and just needs to build the roof to fit. She designs a triangle-shaped roof by using two sheets of wood, forming a 90° angle at the peak. Looking at the front of the dog house, the distance from either wall is 5 feet across. If the triangle portion is symmetrical, what is the distance from the top of the wall portion to the highest part of the triangle peak? Round your answer to the nearest tenth.(1 point)
feet
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WHICH IS THE CORRECT ANSWER AND WHY SOLVE IT CORRECTLY

Answer 1

To find the height of the triangular portion of the roof (the distance from the top of the wall to the peak of the triangle), we can use the properties of a right triangle.

Given that:

• The base of the triangle is the distance across from wall to wall, which is 5 feet. Since the triangle is symmetrical, the two sides of the triangle that form the 90° angle at the peak are each half of the base. Therefore, each side of the base of the triangle is \( \frac{5}{2} = 2.5 \) feet.

• The peak of the triangle is directly above the midpoint of the base (the distance from either wall).

Let \( h \) be the height of the triangle, and we can use the Pythagorean theorem to find \( h \).

The right triangle has:

• One leg (the height) = \( h \)
• The other leg (half of the base) = 2.5 feet
• The hypotenuse (the sloping side of the roof) can be a variable, but we don't need it to calculate the height.

Since we don't have additional information about the hypotenuse, we will assume that height \( h \) is what we want to calculate. The horizontal leg is known (2.5 feet). The hypotenuse is not directly needed for this part, and we can treat it generically unless more information is given.

If we need to calculate height and no length of the hypotenuse is provided, we can't determine a specific numeric value for \( h \) without additional constraints.

1. However, if we are looking for just the height of the triangle above the wall, we need to note that generally, if the triangle's sides extend to make a height, we can determine a general formula or visualize that height would also require a specific side angle or hypotenuse.

If we have to result in just focusing on the horizontal split of the triangle, and inputs given are strictly within a 90° right triangle:

Assuming it is an isosceles triangle formed with 5 feet across, the peak height can often be defined by structural standard drawings based on aesthetics and ratio but traditionally without any specific height as an angle or vertex need determines this.

If you need the common height assumption while retaining requisite Pythagorean forms applied, please define additional lengths if necessary or refer through basic structural designs found through those attributes again as we lack sufficient input.

Let me know if more details or constraints are provided.